The name of Henry's regiment is the 304th. Crane does not reveal its name until Chapter 18 when Henry and Wilson overhear a conversation between their general and another officer. The general is asking the officer what troops are left to fight. The officer replies,

The officer who rode like a cowboy reflected for an instant. “Well,” he said, “I had to order in th' 12th to help th' 76th, an' I haven't really got any. But there's th' 304th. They fight like a lot 'a mule drivers."

Henry and Wilson are astonished to hear their regiment called "mule drivers" but they run back to camp and tell the others to prepare to fight. By not revealing the name of the regiment until they are about to fight is the same technique Crane uses by not revealing Henry's name until after he has fought. It seems as if Crane does not consider a person's identity important until they face losing their identity in the line of duty.